Forecast on S&P 500 Index Barrier Option with BSM Model

Instead of buying the stocks or shares directly, the call option gives a chance for owners to buy it at a specific predetermined price, which prominently decreases the risk for the customers. Thus, it plays a significant role in the economic market and be widely used in a considerable number of financial activities. This paper mainly focuses on forecasting the price of underlying assets and the payoff at maturity for the up-and-in call barrier option. The overall market is the S&P 500 index stock. In this paper, the BSM model is used to simulate the price of the asset in a certain period. After all, the sensitivity tests are applied to identify how many variations in those basic input parameters will impact the results for this model. The test on strike price shows it has an exponential positive relation with payoff; spot price shows a linear negative relation, and barrier price shows no connection with payoff when it's lower than the spot price. Otherwise, it represents a negative relation. Some discussions are also shown about the deficiencies and future studies based on this model in the end.